Draw the neat diagrams for modes of vibration of an air column in a pipe, when
(i) the pipe is open at both ends, and
(ii) the pipe is closed at one end.
Hence derive an expression for fundamental fre-quency in each case.
A horizontal cicular loops of a wire of radius 0.02 m is lowered into crude oil and film is formed. The force due to the surface tension of the liquid is `0.0113 N`. Calculate the surface a tension of the crude oil. `(pi = 3.142)`

Explanation

### Step-by-Step Solution

#### Part 1: Modes of Vibration of an Air Column in a Pipe

**(i) Pipe Open at Both Ends**

1. **Diagram**: Draw a pipe with both ends open. Mark the ends as open.
- At both ends, there are anti-nodes (maximum displacement of air).
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